198edo: Difference between revisions

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'''198 equal temperament''' divides the octave into 198 parts of 6.061 ~~cents~~ each.

The '''198 equal divisions of the octave''' ('''198edo'''), or the '''198(-tone) equal temperament''' ('''198tet''', '''198et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 198 parts of 6.061 [[cent]]s each.

== Theory ==

198edo is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and [[6144/6125]] in the 7-limit; in the [[11-limit]] it tempers [[3025/3024]], [[9801/9800]] and [[14641/14580]]; and in the [[13-limit]] [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]] and [[2080/2079]].

It is the [[optimal patent val]] for the rank ~~five~~ temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka~~]] and [[Canou family #Semicanou|semicanou~~]]. It is distinctly [[consistent]] through the [[15-odd-limit]]. It factors into 2 × 3<sup>2</sup> × 11, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.

It is the [[optimal patent val]] for the rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], and [[Hemifamity family #Namaka|namaka]]. It is distinctly [[consistent]] through the [[15-odd-limit]]. It factors into 2 × 3<sup>2</sup> × 11, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.

=== Prime ~~intervals~~ ===

=== Prime harmonics ===

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[[Category:198edo]]

[[Category:Minthmic]]

[[Category:~~Misty~~]]

[[Category:Namaka]]

[[Category:~~Hemifamity]]~~

[[Category:Semicanou]]

~~[[Category:Canou~~]]

[[Category:Semicanousmic]]

@@ Line 1: / Line 1: @@
-'''198 equal temperament''' divides the octave into 198 parts of 6.061 cents each.
+The '''198 equal divisions of the octave''' ('''198edo'''), or the '''198(-tone) equal temperament''' ('''198tet''', '''198et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 198 parts of 6.061 [[cent]]s each.
 == Theory ==
 edo is contorted in the [[7-limit]], with the same tuning as [[99edo]], but makes for a good 11- and 13-limit system. Like 99, it tempers out [[2401/2400]], [[4375/4374]], [[3136/3125]], [[5120/5103]] and [[6144/6125]] in the 7-limit; in the [[11-limit]] it tempers [[3025/3024]], [[9801/9800]] and [[14641/14580]]; and in the [[13-limit]] [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]] and [[2080/2079]].
-It is the [[optimal patent val]] for the rank five temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], [[Hemifamity family #Namaka|namaka]] and [[Canou family #Semicanou|semicanou]]. It is distinctly [[consistent]] through the [[15-odd-limit]]. It factors into 2 × 3<sup>2</sup> × 11, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.
+It is the [[optimal patent val]] for the rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[Misty family #Hemimist|hemimist]], and [[Hemifamity family #Namaka|namaka]]. It is distinctly [[consistent]] through the [[15-odd-limit]]. It factors into 2 × 3<sup>2</sup> × 11, and has divisors 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99.
-=== Prime intervals ===
+=== Prime harmonics ===
 {{Primes in edo|198|columns=11}}
@@ Line 16: / Line 16: @@
 [[Category:198edo]]
 [[Category:Minthmic]]
-[[Category:Misty]]
+[[Category:Namaka]]
-[[Category:Hemifamity]]
+[[Category:Semicanou]]
-[[Category:Canou]]
 [[Category:Semicanousmic]]